1/2cos(x)+1/2

Input

1/2 cos(x) + 1/2

Series expansion at x=0

1 - x^2/4 + x^4/48 + O(x^5) (Taylor series)
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Derivative

d/dx(cos(x)/2 + 1/2) = -sin(x)/2

Indefinite integral

integral(1/2 + cos(x)/2) dx = 1/2 (x + sin(x)) + constant

Global maxima

max{cos(x)/2 + 1/2} = 1 at x = 2 π n for integer n
POWERED BY THE WOLFRAM LANGUAGE